In this work, we propose a new invariant for 2D persistence modules called the compressed
multiplicity and show that it generalizes the notions of the dimension vector and the rank …

In this work, we propose a new invariant for $2 $ D persistence modules called the
compressed multiplicity and show that it generalizes the notions of the dimension vector and …

In the persistent homology of filtrations, the indecomposable decompositions provide the
persistence diagrams. However, in almost all cases of multidimensional persistence, the …

The incidence coalgebras $ C= K^{□} I $ of intervally finite posets I and their comodules are
studied by means of their Cartan matrices and the Euler integral bilinear form $ b_ {C} …

In the persistent homology of filtrations, the indecomposable decompositions provide the
persistence diagrams. However, in almost all cases of multidimensional persistence, the …

Electronic cash systems are used as payment tools of e-commerce. They should be
equipped with independence, transferability, and dividability, which are requirements of …

We study the complexity of Bongartz's algorithm for determining a maximal common direct
summand of a pair of modules M, N over k-algebra Λ; in particular, we estimate its …

Let A be a finite-dimensional algebra over an algebraically closed field\Bbbk k. For any finite-
dimensional A-module M we give a general formula that computes the indecomposable …

We present combinatorial algorithms for solving three problems that appear in the study of
the degeneration order≤ deg for the variety of finite-dimensional modules over a k-algebra …

Let Λ be the four subspace algebra. We show that for any Λ-module M there exists an
algorithm (up to the problem of finding roots of the so-called characteristic polynomial of M) …